I would imagine it means creating a rainbow table for a particular set of prime numbers. From the article it sounds like many applications use a small handful of prime numbers. A DH key exchange uses two prime numbers (shared publicly) and two secrets (kept, secret...).
In theory the NSA could enumerate ginormous rainbow tables for a large set of secret keys.
Perhaps someone else on HN can provide a more detailed description of the suspected attack?
Edit: the responses to smegel's question below seem much mor e thorough and accurate than mine!
The rainbow table and the attack described here both do a lot of precomputation that can then be re-used for individual attack instances, but the rainbow table is a specific structure that only applies to reversing hashes -- a different problem from computing discrete logarithms.
I think the kind of precomputation you envision here is still too hard to do because the number of possible DH secrets is still much too big to examine all of them by precomputation!
Makes sense. With my primitive understanding I assumed this was why it was so computationally expensive still. But the descriptions by others make much more sense.
In theory the NSA could enumerate ginormous rainbow tables for a large set of secret keys.
Perhaps someone else on HN can provide a more detailed description of the suspected attack?
Edit: the responses to smegel's question below seem much mor e thorough and accurate than mine!